TEST_ZERO
Zero Finder Tests

TEST_ZERO is a MATLAB routine containing a library of nonlinear functions.

The nonlinear functions are intended for use in demonstrating or testing zero finder algorithms, that is, programs that seek a root of a scalar equation F(X)=0.

The MATLAB function TEST_ZERO evaluates one of several scalar nonlinear test functions, and has the form:

        function [ fx, fp ] = test_zero ( x )
      

        global IPROB
      

The functions, which are accessible by number, are

1. f(x) = sin ( x ) - x / 2.
2. f(x) = 2 * x - exp ( - x ).
3. f(x) = x * exp ( - x ).
4. f(x) = exp ( x ) - 1 / ( 10 * x )^2.
5. f(x) = ( x + 3 ) * ( x - 1 )^2.
6. f(x) = exp ( x ) - 2 - 1 / ( 10 * x )^2 + 2 / ( 100 * x )^3.
7. f(x) = x^3.
8. f(x) = cos ( x ) - x.
9. the Newton Baffler.
10. the Repeller.
11. the Pinhead.
12. Flat Stanley.
13. Lazy Boy.
14. the Camel.
15. a pathological function for Newton's method.
16. Kepler's Equation.
17. f(x) = random number.
18. f(x) = x^3 - 2*x - 5, Wallis's function.
19. f(x) = x^2 + 1 + log((x-pi)^2)/pi^4, the "thin pole".

Related Data and Programs:

TEST_ZERO is also available in a FORTRAN90 version.

Reference:

1. George Donovan, Arnold Miller, Timothy Moreland,
   Pathological Functions for Newton's Method,
   American Mathematical Monthly, January 1993, pages 53-58.
2. Peter Colwell,
   Solving Kepler's Equation Over Three Centuries,
   Willmann-Bell, 1993
3. Arnold Krommer, Christoph Ueberhuber,
   Numerical Integration on Advanced Systems,
   Springer, 1994.

Source Code:

• test_zero.m, an implementation of the test functions as a MATLAB function.

You can go up one level to the MATLAB source codes.